In 2HDMs of type II (and Y) a very stringent limit can be set on \(M_{H^\pm }\)  from the flavour observables Br\(({\bar{B}} \rightarrow X_s \gamma )\)  and \(\Delta m_{B_s}\) , as well as from the hadronic \(Z \rightarrow b\bar{b}\)  branching ratio \(R_b\) : \(M_{H^\pm } > 380\)  GeV at 95% CL irrespective of the value of \(\tan \! \beta \)  [1]}, [2]}, [3]}, [4]}. This bound is much stronger than the model-independent one obtained at LEP, \(M_{H^{\pm }} > 79.3\)  GeV at 95% CL [5]}, [6]}. This strong constraint \(M_{H^\pm } > 380\)  GeV, combined with the theoretical requirements shown in Fig. REF , leads to \(M_A \gtrsim 300\)  GeV. In turn, this lower bound on \(M_A\)  is in conflict with the required value for \(\Delta a_\mu \) , as can be seen from Fig. REF . Therefore, type II models are strongly disfavoured by these combined constraints. On the other hand, no such strong flavour bounds on \(M_{H^\pm }\)  exist in type X models [7]}, [3]}. These models are therefore consistent with all the constraints we considered, provided \(M_A\)  is small and \(\tan \! \beta \)  large (see Fig. REF ), \(M_{H^{\pm }} \:\raisebox {-1.1ex}{\stackrel{\textstyle <}{\sim }}\:200\)  GeV (Fig. REF ), and \(M_H \sim M_{H^\pm }\)  (Fig. REF ).
